since beeing killed by the deathnote is not natural death, his normal remaining lifespan should have been some days maybe even less after the time of his death, since near would probably have sentenced him to death.

Well, not completely accurate because Near said that he wasn't going to kill him. He said he was going to completely separate him from the outside world (in other words, keep him imprisoned for life). So who knows how long he would have lived after that if he didn't get caught (if it wasn't for Teru's stupidity).